Fungrim entry: c03f78

R_F\!\left(x, y, z\right) \le \frac{1}{{\left(x y z\right)}^{1 / 6}}

Assumptions:

x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right)

References:

https://dlmf.nist.gov/19.24

TeX:

R_F\!\left(x, y, z\right) \le \frac{1}{{\left(x y z\right)}^{1 / 6}}

x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRF`	$R_F\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the first kind
`Pow`	${a}^{b}$	Power
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("c03f78"),
    Formula(LessEqual(CarlsonRF(x, y, z), Div(1, Pow(Mul(Mul(x, y), z), Div(1, 6))))),
    Variables(x, y, z),
    Assumptions(And(Element(x, OpenInterval(0, Infinity)), Element(y, OpenInterval(0, Infinity)), Element(z, OpenInterval(0, Infinity)))),
    References("https://dlmf.nist.gov/19.24"))

Topics using this entry

Carlson symmetric elliptic integrals